(f) Show that the cartesian equation of this curve is x3 + y³ = 3xy. (g) Show that the polar equation of this curve can be written in the form 3 sec 0 tan 0 r = 1+ tan³ 0 (h) Find the area enclosed by the loop of this curve. Be careful in setting up your integrals. Provide all the details.

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Q: a). Find y' if sin(xr+ y)= y² cos x sin(x+ y)= y° cos x cos X by b). Sketch a graph of

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Q: 1. In this workshop, we are going to explore formulas for areas and arc length associated to curves…

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Q: cos(0) – sin(0) between the lines 0 = 0 and 0 = 4 Find the area under the polar curve r = 5.

A: Explanation of the answer is as follows

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Q: V4-x² e-z²-y² 12. Use a change to polar coordinates to evaluate the integral dy dr.

A: Answer

Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: Evaluate | exp(-2²)dx, using an iterated integral and polar coordinates.

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Q: Find the area of the shaded region of the graph of r=1+sin(0)

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Q: Find the area between 0 = 0 and 0 = π/2 of the polar curve r = 1 + sin 0

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Q: 6. Sketch the curve r=3cos0+2. Find the points at which the curve has a horizontal tangent line.

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Q: Find the surface area resulting from the rotation of the parts in the first and fourth quadrants of…

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